Brightness of distant galaxies problem

In summary: However, in this case, there is a possibility that you might have made a mistake in your calculation.
  • #1
whiterabbit90
4
0

Homework Statement



An object gives out a spectral line of 919nm compared to that of 589nm in a laboratory. It has a brigtness of 1.2 x 10-11 W m-2. The objective is to find out the brightness of the object if it were at 700 Mpc.

Homework Equations



1. Z (redshift)= change in wavelength / original wavelength

2. V= Z X C

3. V= H0D

4. F= L / 4 pi r2


The Attempt at a Solution



The redshift value I find to be 0.56 using equation 1. Using this I calculate the speed as 168000 km s-1 using equation 2. I then work out the distance of the object to be 2400Mpc using equation 3 rearranged. now from here do I use equation 4 to calculate the luminosity and then change the distance to 700Mpc or do I divide 2400Mpc by 700Mpc to get how many times closer the object will be square the answer ( 3.432) and times it by the original brightness 1.2 x 10-11 W m-2?
 
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  • #2
Try both ways and see if they give the same answer or not.
 
  • #3
I tried both, equation 4 gives me an answer of 4.932 x 10-9 and using divide and square i get 1.411 x 10-10 both seem plausible answers.
 
  • #4
In what units?

If they're the units I suspect you meant, one of those answers is wrong - and not just in the obvious sense that they can't both be right; you miscalculated one of them. Go back and check your math.
 
  • #5
both should be in units of W m-2. In equation 4 I converted Mpc to metres same luminosity is Watts. My equation for 4 looks like this rearranged.

L= F x 4 pi r2

Putting in the values gives 1.2 x 10-11 W m-2(F) x 4 pi (7.44x 1025)2 m (r2) = 8.35 x 1041 W (L)

With that I get luminosity to be 8.35 x 1041 W (L)

Using equation 4 as F= L / 4 pi r2 and using the new value for Luminosity I get.

8.35 x 1041 W / (4 pi (2.17 x 1025)2)m2 = 4.932 x 10-9 W m-2

Can anyone tell me where in that I am going wrong as the equations and units all seem to add up if anything I feel this may be the correct answer and the other method using 3.432 may be wrong. However as 3.432 does not have units is shouldn't effect W m-2.
 
  • #6
whiterabbit90 said:
8.35 x 1041 W / (4 pi (2.17 x 1025)2)m2 = 4.932 x 10-9 W m-2
This is the problem. The result of that calculation is not [itex]4.932\times 10^{-9}\frac{\mathrm{W}}{\mathrm{m}^2}[/itex].
 
  • #7
I just calculated it and got 1.411 x 10-10 I think the problem was I was squaring the entire bottom half of the divide rather than the distance. A stupid mistake but guess we all make them. I assume since both equations give the same answer that is the right answer?
 
  • #8
Yeah, everybody makes stupid mistakes ;)

Usually when you can do something two different ways and get the same answer, chances are good that you got it right.
 

1. What is the brightness of distant galaxies problem?

The brightness of distant galaxies problem refers to the challenge scientists face in accurately measuring the brightness of galaxies that are located far away from Earth. This is due to the fact that the light from these galaxies has traveled for billions of years before reaching our telescopes, causing it to be faint and difficult to measure.

2. Why is it important to study the brightness of distant galaxies?

Studying the brightness of distant galaxies allows scientists to gain a better understanding of the universe's evolution and structure. It can also provide insights into the formation and behavior of galaxies, as well as the properties of dark matter and dark energy.

3. How do scientists measure the brightness of distant galaxies?

Scientists use a measurement called apparent magnitude, which is a scale that indicates the brightness of an object as seen from Earth. They also take into account factors such as distance, dust, and the type of galaxy in order to accurately measure its brightness.

4. What challenges do scientists face in measuring the brightness of distant galaxies?

One of the main challenges is the presence of dust and gas in between Earth and the distant galaxy, which can obscure the light and make it more difficult to measure. Another challenge is the varying distances of galaxies, as well as the fact that some galaxies may be intrinsically brighter than others.

5. How can scientists overcome the brightness of distant galaxies problem?

Scientists are constantly developing new technologies and techniques to overcome the challenges of measuring the brightness of distant galaxies. This includes using advanced telescopes and instruments, as well as developing new models and simulations to better understand the behavior of light in the universe.

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